Activity Goals

The goals of this activity are:
1. To be able to write a boolean expression using variables of various types

Feel free to visit these resources for supplemental background reading material.

The Activity

Directions

Consider the activity models and answer the questions provided. First reflect on these questions on your own briefly, before discussing and comparing your thoughts with your group. Appoint one member of your group to discuss your findings with the class, and the rest of the group should help that member prepare their response. Answer each question individually from the activity on the Class Activity Questions discussion board. After class, think about the questions in the reflective prompt and respond to those individually in your notebook. Report out on areas of disagreement or items for which you and your group identified alternative approaches. Write down and report out questions you encountered along the way for group discussion.

Model 1: Representing Truth as a Variable to Make Decisions in Programs

Type
Purpose
Example
&&
AND two booleans (compute true if both are true)
boolean b = false;
boolean x = true && b; // false
||
OR two booleans (compute true if at least one is true)
boolean x = (true || false); // true
!
NEGATE a boolean
boolean x = !(true || false); // = !(true) = false
==
Check if two values are equal
boolean x = (10 == 5); // false
!=
Check if two values are not equal. This is the same as !(x == y)
boolean x = (10 != 5); // true

Questions

1. What is the result of (a || b) && (c || d) if a = true, b = true, c = false, d = false?
2. If a is true in the example above, is it necessary to evaluate b at all?
3. DeMorgan’s Law allows you to simplify a boolean expression by "factoring out" a negation, and flipping an AND to an OR (and vice-versa). For example, (!a && !b) is equivalent to !(a || b). The reverse procedure also works - negating the outside, negating each term on the inside, and flipping the operator: !(a || b) is equivalent to (!a && !b). Re-write !(a && !b) using DeMorgan’s Law.
4. Write a program to compute (!a && !b) for two boolean variables, and then to compute the DeMorgan's Law version of that expression. Try it with all four combinations of boolean variables (true/true, false/false, true/false, false/true), and print both results to verify that they are equivalent.
5. In the Venn diagram above, assign a to the left circle, and b to the right circle. Fill in !a || !b. Now fill in !(a && b). How do they differ?

Embedded Code Environment

You can try out some code examples in this embedded development environment! To share this with someone else, first have one member of your group make a small change to the file, then click "Open in Repl.it". Log into your Repl.it account (or create one if needed), and click the "Share" button at the top right. Note that some embedded Repl.it projects have multiple source files; you can see those by clicking the file icon on the left navigation bar of the embedded code frame. Share the link that opens up with your group members. Remember only to do this for partner/group activities!

Submission

Submit your answers to the questions using the Class Activity Questions discussion board. You may also respond to questions or comments made by others, or ask follow-up questions there. Answer any reflective prompt questions in the Reflective Journal section of your OneNote Classroom personal section.